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9 May, 05:46

Calculate the unit cell edge length for an 87 wt% Ag - 13 wt% Pd alloy. All of the palladium is in solid solution, and the crystal structure for this alloy is FCC. Room temperature densities for Ag and Pd are 10.49 g/cm3 and 12.02 g/cm3, respectively, and their respective atomic weights are 107.87 g/mol and 106.4 g/mol. Report your answer in nanometers. nm

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  1. 9 May, 06:21
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    Since the crystal structure is FCC, every unit cell will have 4 atoms. If a be the edge length

    average density = 4 x average atomic no / volume of unit cell x N

    N is avogadro no or 6.02 x 10²³

    average atomic no

    = 100 / (87/107.9 + 13/106.4) = 107.72

    average density = 100 / (87/10.49 + 13/12.02)

    = 10.667

    10.667 = (4 x 107.72) / (a³x 6.02 x 10²³)

    a³ = 4 x 107.72 / (10.667 x 6.02 x 10²³)

    = 6.71 x 10⁻²³

    a = 4.063 x 10⁻⁸ m
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